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  "problem_id": "vibemathed:ji-zhang-power-set-question",
  "title": "Ji-Zhang Question on the Power Set of a Quasinilpotent Operator",
  "canonical_statement": "Douglas and Yang attach to each nonzero vector $x$ of a quasinilpotent operator $T$ a local resolvent-growth exponent $k_x$, giving the power set $\\Lambda(T) = \\{k_x : x \\ne 0\\}$. Ji and Zhang asked whether $1$ always belongs to $\\Lambda(T)$. It does, for every quasinilpotent operator on every Banach space. Moreover $\\Lambda(T) = [0,1]$ for every backward unilateral weighted shift on $\\ell^p$ with strictly decreasing, $p'$-summable weights, weakening the hypotheses of Hu and Ji.",
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      "occurred_at": "2026-07-18T00:00:00.000Z",
      "title": "arXiv:2607.16743 - The power set of a quasinilpotent backward weighted shift",
      "summary": "VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
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      "attempted_at": "2026-07-18T00:00:00.000Z",
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      "outcome": "The declaration states that generative AI was used substantially, and that its contribution was decisive for the formulation and proof of Lemma 1 in particular, with further help drafting several of the standard arguments and the LaTeX source. All output was produced under the author's direction and subsequently revised and verified by him.",
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